Interactions obtained from basic mechanistic principles : prey herds and predators

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Berardo , C , Bulai , I M & Venturino , E 2021 , ' Interactions obtained from basic mechanistic principles : prey herds and predators ' , Mathematics , vol. 9 , no. 20 , 2555 . https://doi.org/10.3390/math9202555

Title: Interactions obtained from basic mechanistic principles : prey herds and predators
Author: Berardo, Cecilia; Bulai, Iulia Martina; Venturino, Ezio
Contributor: University of Helsinki, Department of Mathematics and Statistics
Date: 2021-10-12
Language: eng
Number of pages: 18
Belongs to series: Mathematics
ISSN: 2227-7390
URI: http://hdl.handle.net/10138/335497
Abstract: We investigate four predator–prey Rosenzweig–MacArthur models in which the prey exhibit herd behaviour and only the individuals on the edge of the herd are subjected to the predators’ attacks. The key concept is the herding index, i.e., the parameter defining the characteristic shape of the herd. We derive the population equations from the individual state transitions using the mechanistic approach and time scale separation method. We consider one predator and one prey species, linear and hyperbolic responses and the occurrence of predators’ intraspecific competition. For all models, we study the equilibria and their stability and we give the bifurcation analysis. We use standard numerical methods and the software Xppaut to obtain the one-parameter and two-parameter bifurcation diagrams.
Subject: 111 Mathematics
1181 Ecology, evolutionary biology
predator-prey model
herd behaviour
herd shape
linear functional respons
Holling type II functional response
bifurcation analysis
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